Related papers: A Survey on Small-Area Planar Graph Drawing
Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…
Let $G$ be a planar $3$-graph (i.e., a planar graph with vertex degree at most three) with $n$ vertices. We present the first $O(n^2)$-time algorithm that computes a planar orthogonal drawing of $G$ with the minimum number of bends in the…
We propose a new exact approach to the generalized graph layering problem that is based on a particular quadratic assignment formulation. It expresses, in a natural way, the associated layout restrictions and several possible objectives,…
Untangling is a process in which some vertices of a planar graph are moved to obtain a straight-line plane drawing. The aim is to move as few vertices as possible. We present an algorithm that untangles the cycle graph C_n while keeping at…
Do algorithms for drawing graphs pass the Turing Test? That is, are their outputs indistinguishable from graphs drawn by humans? We address this question through a human-centred experiment, focusing on `small' graphs, of a size for which it…
Large graphs can be found in a wide array of scientific fields ranging from sociology and biology to scientometrics and computer science. Their analysis is by no means a trivial task due to their sheer size and complex structure. Such…
This is a survey article for the forthcoming `A Concise Encyclopedia of Knot Theory.' We focus on the topology of spatial graphs with few vertices and edges, paying particular attention to Brunnian $\theta$-graphs.
Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…
Contact graphs of isothetic rectangles unify many concepts from applications including VLSI and architectural design, computational geometry, and GIS. Minimizing the area of their corresponding {\em rectangular layouts} is a key problem. We…
We discuss the problem of embedding graphs in the plane with restrictions on the vertex mapping. In particular, we introduce a technique for drawing planar graphs with a fixed vertex mapping that bounds the number of times edges bend. An…
Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity…
Autonomous robotic inspection, where a robot moves through its environment and inspects points of interest, has applications in industrial settings, structural health monitoring, and medicine. Planning the paths for a robot to safely and…
Optimal linear-time algorithms for testing the planarity of a graph are well-known for over 35 years. However, these algorithms are quite involved and recent publications still try to give simpler linear-time tests. We give a simple…
A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…
We give lower bounds for various natural node- and edge-based local strategies for exploring a graph. We consider this problem both in the setting of an arbitrary graph as well as the abstraction of a geometric exploration of a space by a…
This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…
Orthogonal graph drawing has many applications, e.g., for laying out UML diagrams or cableplans. In this paper, we present a new pipeline that draws multigraphs orthogonally, using few bends, few crossings, and small area. Our pipeline…
We study the problem of drawing a dynamic graph, where each vertex appears in the graph at a certain time and remains in the graph for a fixed amount of time, called the window size. This defines a graph story, i.e., a sequence of…
Spatial graphs are particular graphs for which the nodes are localized in space (e.g., public transport network, molecules, branching biological structures). In this work, we consider the problem of spatial graph reduction, that aims to…
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show the surprising fact that it is NP-hard to compute the crossing number of near-planar graphs. A graph is 1-planar if it has a drawing where every…